1 Accurate dynamical mass determination of a classical Cepheid in an eclipsing binary system G. Pietrzyński1,2, I.B. Thompson3 ,W. Gieren1, D. Graczyk1, G. Bono4,5, A. Udalski2, I. Soszyński2, D. Minniti6 , B. Pilecki1,2 1. Universidad de Concepción, Departamento de Astronomìa, Casilla 160-C, Concepciòn, Chile 2. Obserwatorium Astronomiczne Uniwersytetu Warszawskiego, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland 3. Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 911101-1292, USA 4. Dipartimento di Fisica Universita’ di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Rome, Italy 5. INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monte Porzio Catone, Italy 6. Pontificia Universidad Católica de Chile, Departamento de Astronomía y Astrofísica, Casilla 306, Santiago 22, Chile Stellar pulsation theory provides a means of determining the masses of pulsating classical Cepheid supergiants—it is the pulsation that causes their luminosity to vary. Such pulsational masses are found to be smaller than the masses derived from stellar evolution theory: this is the Cepheid mass discrepancy problem (1,2), for which a solution is missing (3–5). An independent, accurate dynamical mass determination for a classical Cepheid variable star (as opposed to type-II Cepheids, low-mass stars with a very different evolutionary history) in a binary system is needed in order to determine which is correct. The accuracy of previous efforts to establish a dynamical Cepheid mass from Galactic single-lined non- eclipsing binaries was typically about 15–30 per cent (refs 6, 7), which is not good 2 enough to resolve the mass discrepancy problem. In spite of many observational efforts (8,9), no firm detection of a classical Cepheid in an eclipsing double-lined binary has hitherto been reported. Here we report the discovery of a classical Cepheid in a well detached, double-lined eclipsing binary in the Large Magellanic Cloud. We determine the mass to a precision of one per cent and show that it agrees with its pulsation mass, providing strong evidence that pulsation theory correctly and precisely predicts the masses of classical Cepheids. In the course of the OGLE microlensing survey conducted by several members of our We have detected several candidates for Cepheid variables in eclipsing binary systems in the Large Magellanic Cloud (10) (LMC). Using high-resolution spectra, we confirmed the discovery of a classical fundamental-mode Cepheid pulsator OGLE- LMC-CEP0227 in a well detached, double-lined, eclipsing system with near-perfect properties for deriving the masses of its two components with very high accuracy. (We obtained the spectra with the MIKE spectrograph at the 6.5-m Magellan Clay telescope at the Las Campanas Observatory in Chile, and with the HARPS spectrograph attached to the 3.6-m telescope of the European Southern Observatory on La Silla.) A finding chart for the system can be found on the OGLE Project webpage (10). Our spectroscopic and photometric observations of the binary system are best fitted by assuming a mass ratio of 1.00 for the two components (Fig. 1). This value was used to disentangle the pulsational and orbital radial-velocity variations of the Cepheid component of the binary. The resulting orbital radial-velocity curves of the components, and the pulsational radial-velocity curve of the Cepheid, are shown in Fig. 2. The spectroscopic and photometric observations were then analyzed using the 2007 version of the standard Wilson Devinney code (11,12). We accounted for the photometric variations of the Cepheid caused by the pulsations, as follows. First, we fitted a Fourier series of order 15 to the observations secured outside the eclipses. Second, we subtracted the corresponding variations in the eclipses in an iterative way, scaling the 3 obtained fit according to the resulting Wilson–Devinney model. The I-band pulsational and orbital light curves, together with the best model obtained from the Wilson– Devinney code, are shown in Fig. 3. The corresponding astrophysical parameters of our system are presented in Table 1. The mean radius of the primary (Cepheid) component that we obtained from our binary analysis shows excellent agreement with the radius predicted for its period from the Cepheid period–radius relation of ref. (13) (32.3 solar radii), strengthening our confidence in our results. In order to assign realistic errors to the derived parameters of our system, we performed Monte Carlo simulations. Our analysis of the very accurate existing data sets for OGLE-LMC-CEP0227 has resulted in a purely empirical determination of the dynamical mass of a classical Cepheid variable, with an unprecedented accuracy of 1%. We note that an end-to-end simultaneous solution for all parameters might reveal slightly different uncertainties, and would also illuminate the correlations in the uncertainties between the various derived quantities. From an evolutionary point of view, we have captured our system in a very short-lasting evolutionary phase, when both components are burning helium in their cores during their return from their first crossing of the Cepheid instability strip in the Hertzsprung– Russell diagram. The secondary component is slightly more evolved (it is larger and cooler), and is located just outside the Cepheid instability strip, so it is non-variable. It is very important to note that OGLE-LMC-CEP0227 is a classical, high-mass Cepheid, and not a low-mass type-II Cepheid. This is clearly indicated by both its mass (Table 1) and its position on the period– luminosity diagram for OGLE Cepheids shown in Fig. 4 (which furthermore suggests that the star is a fundamental mode pulsator). Fundamental mode pulsation is also suggested by the strongly asymmetrical shapes and large amplitudes of the pulsation radial-velocity curve and of the I-band light curve (Figs 2 and 3). Of the three candidates for Cepheids in eclipsing binary systems detected 4 earlier by the MACHO and OGLE projects (8,9), the objects MACHO-78.6338.24 and MACHO-6.6454.5 are type-II (low-mass) Cepheids8,10; only the object OGLE-LMC_SC16-119952 (MACHO-81.8997.87) still appears to be a candidate for a classical Cepheid pulsating in the first overtone (14). However, there are currently several problems with the correct interpretation of this last object (9,14), and clearly more photometric and spectroscopic data are needed in order to reveal the true nature of this interesting system and eventually use it for a mass determination for a first overtone classical Cepheid. We also note that the type-II Cepheid MACHO-6.6454.5 belongs to the class of peculiar W Virginis stars introduced in ref. 15. To estimate the pulsation mass of the Cepheid in LMC-OGLE- CEP0227, we adopted a period–mass relation based on nonlinear, convective Cepheid models constructed for the typical chemical com- position of LMC Cepheids (metallicity Z = 0.008, helium mass fraction Y = 0.256) (refs 5, 16, 17). This yields a pulsation mass of Mp = 3.98 ± 0.29 solar masses for the star, which is independent of the assumed reddening and distance of the Cepheid and agrees within 1 σ with its dynamical mass, providing strong evidence that the pulsation mass of a Cepheid variable is indeed correctly measuring its true, current mass. This result contributes significantly to settling the controversy about classical Cepheid masses. The overestimation of Cepheid masses by stellar evolution theory may be the consequence of significant mass loss suffered by Cepheids during the pulsation phase of their lives—such loss could occur through radial motions and shocks in the atmosphere (18,19). 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